Abstract
The paper has two aims. First, a review of various definitions of probabilities on Atanassov IF-sets, and corresponding representation theorems. Secondly, a new representation theorem is proved for so-called ϕ-probabilities including a large variety of special cases.
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Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica Verlag, New York (1999)
Atanassov, K.: Riečan, B: On two new types of probability theory on IF-events. Notes on IFS (2007)
Ciungu, L.: Riečan, B.: General for of probabilities on IF-sets. Information Science (submitted)
Čunderlíková, K., Riečan, B.: Intuitionistic fuzzy probability theory. Edited volume on Intuitionistic Fuzzy Sets: recent Advances of the series Studies on Fuzziness and Soft Computing. Springer, Heidelberg (2008)
Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer, Dordrecht (2000)
Gerstenkorn, T., Manko, J.: Probabilities of intuitionistic fuzzy events. In: Hryniewicz, O., et al. (eds.) Issues in Intelligent Systems: Paradigms, pp. 63–68. EXIT, Warszawa (2005)
Grzegorzewski, P., Mrowka, E.: Probability of intuitionistic fuzzy events. In: Grzegorzewski, P., et al. (eds.) Soft Methods in Probability, Statistics and data Analysis, pp. 105–115. Physica Verlag, New York (2002)
Krachounov, M.: Intuitionistic probability and intuitionistic fuzzy sets. In: El-Darzi, et al. (eds.) First Intern. Workshop on IFS, pp. 714–717. Univ. Of Westminster, London (2006)
Renčová, M.: On the ϕ-probability and ϕ-observables. Fuzzy Sets and Systems (submitted)
Renčová, M.: General form of strongly additive ϕ-probability. In: Magdalenca, L., et al. (eds.) Proc. IPMU 2008, pp. 1671–1674 (2008)
Riečan, B.: A descriptive definition of the probability on intuitionistic fuzzy sets. In: Wagenecht, M., Hampet, R. (eds.) Proc. EUSFLAT 2003, Zittau-Goerlitz Univ. Appl. Sci, Dordrecht, pp. 263–266 (2000)
Riečan, B.: Representation of probabilities on IFS events. In: López-Diaz, M., et al. (eds.) Advances in Soft Computing, Soft Methodology and Random Information Systems, pp. 243–246. Springer, Berlin (2004)
Riečan, B.: On a problem of Radko Mesiar: general form of IF - probabilities. Fuzzy sets and Systems 157, 1485–1490 (2006)
Riečan, B.: On the entropy of IF dynamical systems. In: Proc. IWIFSGN 2005, Warszawa, September 16, 2005, pp. 328–336 (2005)
Riečan, B.: Probability theory on IF events. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds.) ManyVal 2006. LNCS, vol. 4460, pp. 290–308. Springer, Heidelberg (2007)
Riečan, B.: - Mundici, D.: Probability on MV-algebras. In: Pap, E. (ed.) Hanbook on Measure Theory, pp. 869–909. Elsevier, Amsterdam (2002)
Riečan, B., Neubrunn, T.: Integral, Measure, and Ordering. Kluwer, Dordrecht (1997)
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Ciungu, L., Riečan, B. (2009). General Form of Probabilities on IF-Sets. In: Di Gesù, V., Pal, S.K., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2009. Lecture Notes in Computer Science(), vol 5571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02282-1_13
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DOI: https://doi.org/10.1007/978-3-642-02282-1_13
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